🚀 go-pugleaf

ROBERT FIRTH WRITES:

>In article <1992Aug5.062852.5646@sbcs.sunysb.edu> rscott@csws4.ic.sunysb.edu
>  (Robert Scott) writes:
>>THE KINEMATICS OF SPECIAL RELATIVITY IS SIMPLE COMMON SENSE, A SIMPLE AND
>>INEVITABLE RESULT OF SPEED-OF-LIGHT DELAYS.  (ROBERT FIRTH AND DARYL
>>MCCULLOUGH HAVE EXPLAINED THIS RATHER CLEARLY MANY TIMES HERE ON SCI.PHYSICS,
>>I THOUGHT.)
>
>Thank you for the endorsement, but I must regretfully disclaim the
>opinion you attribute to me.  Yes, I believe that a lot of SR is
>much less mystical and paradoxical than many people suppose - for
>example, the 'Barn and Pole' paradox that I wrote up for the FAQ
>list seems to me a simple matter of clear postulates plus common
>sense (too bad the editor changed the original numbers).
>
>However, I do not believe all of SR can be explained by signal
>delays.  If I did, I'd be a happier camper.  For me, the crux
>is the phenomenon called time dilation.  As far as I know, it's
>real, it's been observed, there is no good explanation for it
>other than SR, and, most important, it is a phenomenon whose
>consequences (slow clocks) persist even after everything has
>been brought to relative rest and all signals have got wherever
>they were going.  If Howard Hayden or whoever can pull down
>that pillar, the whole edifice will collapse; but so far I
>see a lot of straining and grunting, and few signs of imminent
>structural failure.  But hope is perenneal, as my $25 cheques
>to Galilaean Electrodynamics are annual.


WELL, MAYBE I DIDN'T MAKE MYSELF CLEAR.  I WASN'T TRYING TO SAY THAT
THE ORTHODOX VERSION OF SPECIAL RELATIVITY IS WRONG AND THAT IT NEEDS
TO BE REPLACED BY A COMMON-SENSE VERSION IN WHICH EVERYTING IS
EXPLAINED AS A SIMPLE RESULT OF SPEED-OF-LIGHT DELAYS.  RATHER, I WAS
TRYING TO SAY THAT THE ORTHODOX VERSION OF SPECIAL RELATIVITY _IS_ A
COMMON-SENSE VERSION IN WHICH EVERYTHING IS EXPLAINED AS A SIMPLE
RESULT OF SPEED-OF-LIGHT DELAYS, REGARDLESS OF HOW MUCH SOME TEACHERS
AND TEXTBOOKS TRY TO OBFUSCATE THIS POINT.  AS FOR THE "GALILIEAN
ELECTRODYNAMICS" PEOPLE, I REALLY DON'T KNOW VERY MUCH ABOUT THEM, BUT
IF THEY ARE TRYING TO ARGUE THAT GALILEAN INVARIANCE IS A MORE USEFUL
ORGANIZING PRINCIPLE IN PHYSICS THAN LORENTZIAN INVARIANCE IS, THEN
THAT SOUNDS LIKE A VERY FOOLHARDY THING TO ATTEMPT.  (ACTUALLY I
SUSPECT THAT THEY ARE TRYING TO DO SOMETHING ELSE ALTOGETHER, BUT I
HAVE VERY LITTLE INTEREST IN FINDING OUT WHAT IT IS.)

ONE OF THE IDEAS THAT I'VE TOYED AROUND WITH FOR TRYING TO HELP
STUDENTS UNDERSTAND HOW SPEED-OF-LIGHT DELAYS LEAD INEXORABLY TO
SPECIAL RELATIVITY IS A COMPUTER GAME MODELLED AFTER AN OLD COMPUTER
GAME CALLED "ROBOT WARS".  ALTHOUGH "ROBOT WARS" HAD ITS SHARE OF
MECHANICAL VIOLENCE, IT WAS NOT A TYPICAL MINDLESS
INSTANT-GRATIFICATION GAME; RATHER, THE PLAYERS WOULD WRITE PROGRAMS IN
A SIMPLE PROGRAMMING LANGUAGE TO ANIMATE ROBOTS LIVING IN A VERY
PRIMITIVE LITTLE VIRTUAL WORLD, AND THEN THE PLAYERS WOULD SIT AROUND
AND WATCH THE ROBOTS FIGHT AGAINST EACH OTHER ON THE VIDEO SCREEN.  IN
MY VERSION, THE ROBOTS WOULD BE PARTNERS RATHER THAN OPPONENTS, AND THE
GOAL OF THE GAME WOULD BE TO GET THE ROBOTS TO EXECUTE FORMATIONS IN
THE STYLE OF A TEAM OF AEROBATIC AIRPLANES.  BUT THE LAWS OF PHYSICS IN
THIS VIRTUAL WORLD WOULD BE SPECIAL RELATIVISTIC, NOT BY MASSIVE
CONTRIVANCE, BUT SIMPLY BY VIRTUE OF RESTRICTING ALL SIGNALS TO TRAVEL
AT LIGHT-SPEED (AND DOING NOTHING ELSE TO BREAK THE SYMMETRY ANY
FURTHER).  THEN STUDENTS WOULD LEARN BY BUTTING THEIR HEADS UP AGAINST
MATHEMATICAL REALITY THAT EVEN THOUGH A FLEET OF ROBOTS CAN BE
PROGRAMMED TO EXECUTE VERY INTRICATE AND INTERESTING FORMATIONS, THERE
IS, FOR EXAMPLE, NO WAY TO PROGRAM THEM SO THAT, STARTING FROM RANDOM
POSITIONS IN SPACE-TIME AND RANDOM SUB-LIGHT-SPEED VELOCITIES, THEY ARE
ABLE TO ORIENT THEMSELVES RELATIVE TO EACH OTHER AND THEN ACHIEVE
DISTANT SYNCHRONIZATION OF ACTION.  SIMILARLY THEY WOULD LEARN THAT ANY
ATTEMPT TO PROGRAM THE ROBOTS TO ASSUME A FORMATION OF A PARTICULAR
RIGID SHAPE WOULD BE VULNERABLE TO CONTRACTION OF THE SHAPE IN THE
DIRECTION OF MOTION.  THUS THEY WOULD LEARN ABOUT SPECIAL RELATIVITY IN
A VERY VISCERAL BUT ALSO VERY INTELLECTUAL WAY.

TO BE MORE SPECIFIC ABOUT HOW THIS GAME PROGRAM WOULD WORK: IN
ADDITION TO UNLIMITED INSTANTANEOUS CALCULATION ON AN INTERNAL
SCRATCHPAD, EACH ROBOT WOULD BE ABLE TO SELECT FROM AMONG JUST THE
FOLLOWING PRIMITIVE OPERATIONS:

1.  BROADCAST A MESSAGE.  ALL MESSAGES TRAVEL AT ONE FIXED SPEED, CALLED 
"LIGHT-SPEED".

2.  WAIT FOR AND THEN READ A MESSAGE.

3.  WAIT FOR AN EVENT DEFINED AS AN AFFINE COMBINATION OF THE POINTS OF 
ORIGIN OF PREVIOUSLY RECEIVED MESSAGES.

4.  SELECT A NEW VELOCITY, SPECIFIED AS THE VELOCITY THAT WOULD BE
NEEDED TO TRAVEL FROM EVENT X TO EVENT Y, WHERE X AND Y ARE AFFINE
COMBINATIONS OF THE POINTS OF ORIGIN OF PREVIOUSLY RECEIVED MESSAGES.  
IF X=Y OR IF THE SPECIFIED VELOCITY IS LIGHT-SPEED OR GREATER, THEN THE
COMMAND IS IGNORED.

THE VIDEO DISPLAY WOULD GIVE AN "OMNIPRESENT GOD'S EYE" VIEW OF
ABSOLUTE SPACE.  THE ROBOTS THEMSELVES WOULD APPEAR AS HIGHLY VISIBLE
MOVING DOTS WITH NO SIGNIFICANT SPATIAL EXTENSION, AND BROADCASTED
MESSAGES WOULD APPEAR AS DIMLY VISIBLE EXPANDING SPHERES.  IT WOULD BE
GOOD TO BE ABLE TO SET THE NUMBER OF SPATIAL DIMENSIONS TO EITHER ONE,
TWO, OR THREE.

NOTICE HOW SIMILAR THE PREDICAMENT OF THE ROBOTS IS TO THE PREDICAMENT
THAT ORDINARY MATTER FINDS ITSELF IN EVERY DAY, HELPLESS TO DO ANYTHING
BUT EXHIBIT ALL THE CLASSIC SYMPTOMS OF SPECIAL RELATIVITY.  NOTICE FOR
EXAMPLE HOW EASY IT IS IN THE CASE OF ONE SPATIAL DIMENSION TO PROGRAM
A PAIR OF ROBOTS TO SIMULATE A RELATIVISTIC ELASTIC COLLISION BETWEEN
PARTICLES OF DIFFERENT REST MASS, AND HOW IMPOSSIBLE IT IS TO PROGRAM
THEM TO SIMULATE A NON-RELATIVISTIC COLLISION.

AS FOR YOUR COMPLAINT THAT LIGHT-SPEED DELAYS CAN NOT EXPLAIN WHY
TIME-DILATION OCCURS, I THINK THAT YOU GOT IT EXACTLY BACKWARDS.  THAT
IS, IT'S NOT THAT THE ROBOTS IN THE GAME DON'T EXHIBIT TIME-DILATION;
RATHER IT'S THAT THERE ISN'T EVEN ANY STANDARD AGAINST WHICH YOU CAN
ASK WHETHER THEIR TIME IS DILATED.  THAT IS, THE SYMMETRY GROUP
OPERATING HERE, WHICH IS THE INTERSECTION OF THE GROUP OF AFFINE
TRANSFORMATIONS (PRESERVING THE STRUCTURE RELATED TO INERTIAL MOTION
AND THE SPECIFICATION OF SPACE-TIME POINTS IN TERMS OF AFFINE
COMBINATIONS) AND THE GROUP OF "LORENTZIAN CONFORMAL" TRANSFORMATIONS
(PRESERVING THE STRUCTURE RELATED TO THE LIGHT-SPEED SIGNALLING
PROTOCOL) IS ALMOST, BUT NOT QUITE, JUST THE POINCARE GROUP OF SPECIAL
RELATIVITY.  IT HAS ONE EXTRA DIMENSION, CONSISTING OF THE GROUP OF
UNIFORM EXPANSIONS OF SPACE-TIME ABOUT AN ARBITRARY REFERENCE POINT. 
NEVERTHELESS, I STILL THINK THAT THE EXPERIENCE OF LIVING IN THIS SORT
OF VIRTUAL WORLD CONVEYS ALMOST ALL OF THE FLAVOR OF WHAT SPECIAL
RELATIVITY IS LIKE.  THE EXTRA EXPANSION SYMMETRY IS VERY EASY TO
UNDERSTAND (DESPITE THE RARITY OF TRUE EXPANSION SYMMETRY IN NATURE, AS
ILLUSTRATED FOR EXAMPLE BY GALILEO'S ANALYSIS OF WHY IT IS UNHEALTHY
FOR AN ANIMAL FOR IT TO GROW TOO BIG), AND ONCE YOU'VE GOTTEN USED TO
LIVING WITH [POINCARE+EXPANSION] SYMMETRY IT'S ALSO FAIRLY EASY TO
UNDERSTAND HOW JUST THE EXPANSION SYMMETRY CAN BE BROKEN BY THE
INTRODUCTION OF CLOCKS WHICH KEEP A STANDARD PROPER TIME (AS CONTRASTED
TO A STANDARD TIME VALID IN ALL REFERENCE FRAMES, WHICH WOULD OF COURSE
BREAK THE SYMMETRY MUCH FURTHER).


-JAMES DOLAN